I had mentioned:
To which Logan responded, with actual formulas and stuff!
Thanks! This is one of those moments I really love our little community. Even if I don’t know the answer to a problem, someone else is more than willing to step in to provide!
I was at work when I posted my other reply, so I couldn’t get at my machine settings. Now that I’m home, I was able to open GC on my laptop and check my them. I drew up a quick diagram of the top beam of my machine in relation to the bed, and then overlaid the chains to mock up the position of the sled:
So, in the absolute, worst case scenario, if the bit was literally at the top of the bed, I would have 140.56 degrees of separation between the chains.
So to solve if:
m = 18 kg (~40 lbs)
a = 140.56 deg
F = (m x 0.5) ÷ cos(a x 0.5)
F = (18 x 0.5) ÷ cos(140.56 x 0.5)
F = 9 ÷ cos(70.28)
F = 9 ÷ 0.3374
F = 26.673 kg, or 58.8039 lbs.
So the load forces are 7 lbs lighter on my motors than the stock frame, which are cited around 65 lbs. I had initially been worried that I could be overloading the motors with my heavier sled, but after doing the math it doesn’t seem like that really is an issue.
The big take away from this is that I will have to be careful extending the length of the top beam and therefore the motor spacing. If I simply increase the beam length to 12 feet, my math says that will be 76 lbs at the motors, which is well beyond their stall load. So I would need to 1) raising the height of the beam, or 2) reduce the weight of the sled. I think that 2) would be the easiest solution to the problem, because reducing the sled to the stock 30 lbs puts ~60 lbs to the motors.
However, I think if greater accuracy is the goal, 1) would be the better solution to the problem. I can see there being a trade-off where adding too much height would introduce greater chain sag, so this may have to be tested to find its optimal ratio. But to me, I can image that in the areas where there are the most tension on the sled could introduce more error. So having the motors higher would reduce the amount of tension pulling at either side of the sled.
Or I’m completely off and we’ll all be laughing about this in an hour anyways